Weak solutions to a Penrose-Fife model with Fourier law for the temperature
type: Item
instance of: scholarly article
title: Weak solutions to a Penrose-Fife model with Fourier law for the temperature
zbMATH Open document ID: 0919.35137
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-08-29T00:00:00Z
review text: The author considers an initial-boundary value problem for the system \[ \tau \varphi_t - \xi^2 \Delta\varphi + a (\varphi^3 - \varphi) = b/\theta, \qquad c\theta_t - K \Delta \theta = b \varphi_t \] in \(N\leq 3\) space dimensions, where \(a,b,c,\theta,\xi,K\) are constants. Under the assumption that the initial temperature is positive almost everywhere, he proves the existence of a global weak solution with \(\theta > 0\) almost everywhere.
reviewed by: Martin Brokate
Mathematics Subject Classification ID: 35Q72
Mathematics Subject Classification ID: 35D05
Mathematics Subject Classification ID: 35K50
zbMATH DE Number: 1215739
zbMATH Keywords: Penrose-Fife model
zbMATH Keywords: global weak solution
author: Philippe Laurençot
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5813
OpenAlex ID: W2040055309
cites work: Q4284440
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DOI: 10.1006/JMAA.1997.5813
description: scientific article; zbMATH DE number 1215739